In this discussion, you will use an Excel data set containing the "width percentage" of a group of perch, a type of fish. The width percentage is found by multiplying the width by one hundred, then dividing the result by the length. The mean of the data set is 16.18 and the standard deviation is 1.13. Using a java applet provided by Duxberry Press (©1999), we analyzed the probabilities for a normal distribution of this data set.

Probability is a key concept in statistical hypothesis testing. Let's say you are fishing and catch a fish with a width percentage of 13.3. Since it has an unusual width percentage for a perch, it seems unlikely this fish is a perch. It is too thin! Pretend this width percentage is the only information we have about the fish and we want to decide as best we can whether or not you caught a perch. The logic we use in hypothesis testing is as follows. So, we reject the null and conclude our fish is not a perch (but we realize we might be mistaken). Note that we would also reject the null if the width percentage had been unusually large, for example 18.5. Finally, if the width percentage was in the usual range for a perch, say 15.3, then we would be unable to conclude anything about the fish. We simply have no evidence that the fish is not a perch. In hypothesis testing we say that we retain the null hypothesis. This doesn't show that the fish is a perch though. 


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